Question

the diagram below shows a rhombus:
find the measures of the following variables:

x=

y=

Explanation:

Step1: Use the property of a rhombus

In a rhombus, all sides are equal. So \(AB = BC = CD = DA\).
Since \(AB = 17\), \(BC=3x + 11\), we have the equation \(3x+11 = 17\).

Step2: Solve for \(x\)

Subtract \(11\) from both sides of the equation \(3x+11 = 17\):
\(3x=17 - 11\), so \(3x = 6\).
Divide both sides by \(3\): \(x=\frac{6}{3}=2\).

Step3: Solve for \(y\)

Since \(AD = 7y + 3\) and \(AD=AB = 17\), we have the equation \(7y+3 = 17\).
Subtract \(3\) from both sides: \(7y=17 - 3\), so \(7y = 14\).
Divide both sides by \(7\): \(y=\frac{14}{7}=2\).

Answer:

\(x = 2\); \(y = 2\)